Physical Principles of Electron Microscopy: An Introduction to TEM ...

112 Chapter 4
Unfortunately, the value of L is sensitive to small differences in specimen
height (relative to the objective-lens polepieces) and to magnetic hysteresis
of the TEM lenses, such that a given lens current does not correspond to a
unique magnetic field or focusing power. Electron diffraction is therefore of
limited accuracy: d-spacings can be measured to about 1%, compared with a
few parts per million in the case of x-ray diffraction (where no lenses are
used). However, x-ray diffraction requires a macroscopic specimen, with a
volume approaching 1 mm 3 . In contrast, electron-diffraction data can be
obtained from microscopic volumes (< 1 �m 3 ) by use of a thin specimen and
an area-selecting aperture or by focusing the incident beam into a very small
probe. Electron diffraction has been used to identify sub-micrometer
precipitates in metal alloys, for example.
Some materials such as silicon can be fabricated as single-crystal
material, without grain boundaries. Others have a crystallite size that is
sufficiently large that a focused electron beam passes through only a single
grain. In these cases, there is no azimuthal randomization of the diffraction
spots: the diffraction pattern is a spot pattern, as illustrated in Fig. 4-12d.
Equation (4.22) still applies to each spot, R being its distance from the
central (0 0 0) spot. In this case, the symmetry of the diffraction spots is
related to the symmetry of arrangement of atoms in the crystal. For example,
a cubic crystal produces a square array of diffracted spots, provided the
incident beam travels down one of the crystal axes (parallel to the edges of
the unit cell). Using a double-tilt specimen holder, a specimen can often be
oriented to give a recognizable diffraction pattern, which helps toward
identifying the phase and/or chemical composition of small crystalline
regions within it.
4.8 Diffraction Contrast within a Single Crystal
Close examination of the TEM image of a polycrystalline specimen shows
there can be a variation of electron intensity within each crystallite. This
diffraction contrast arises either from atomic-scale defects within the crystal
or from the crystalline nature of the material itself, combined with the wave
nature
of the transmitted electrons, as we will now discuss.
Defects in a crystal, where the atoms are displaced from their regular
lattice-site positions, can take several different forms. A dislocation is an
example of a line defect. It represents either the termination of an atomic
plane within the crystal (edge dislocation) or the axis of a “spiral staircase”
where the atomic planes are displaced parallel to the dislocation line (screw
dislocation). The structure of an edge dislocation is depicted in Fig. 4-14,
which shows how planes of atoms bend in the vicinity of the dislocation